parmenides51 wrote: Let $a_1,a_2,..., a_n$ be real numbers such that $a_1 + a_2 + ... + a_n = 0$ and $|a_1| + |a_2 | + ... + |a_n | = 1$. Prove that $$ |a_1 + 2a_2 + ... + na_n | \le \frac{n-1}{2} $$ https://artofproblemsolving.com/community/c6h299899p1886089 https://artofproblemsolving.com/community/c1068820h2132619p15598394 https://artofproblemsolving.com/community/c6h1849998p12474392 https://artofproblemsolving.com/community/c6h1078990p4729324